To parse HTML I usually use HTML::TokeParser instead of HTML::TreeBuilder. The latter seems to me too overkill for most problems. This is probably how you can do the parsing with HTML::TokeParser:

use HTML::TokeParser;

my $p = HTML::TokeParser->new("index.html") ||
      die "Can't open: $!";

while (my $token = $p->get_token) {
  if ($token->[0] eq 'td') {
    my $txt = $p->get_trimmed_text;
    if ($txt eq "the text before what you're looking for") {
      $token = $p->get_token("td");
      my $txt = $p->get_trimmed_text;
      # $txt will be the text you're looking for
    }
  }  
}
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